[Statistical approach: classification, signal analysis, features] https://www.youtube.com/watch?v=SgPtGOqACUM&t=3s; 1.1. "Naive" Bayes; 10:28; Demonstration of some functions of the main module of the program. Solving the problem of identifying images of the keyboard handwriting of 32 subjects based on the sequential application of the Bayes hypothesis formula. Estimation of the probabilities of errors of the 1st and 2nd types. Plotting error graphs (ROC curves) https://www.youtube.com/watch?v=4Nqs_2psU5M&t=2s; 1.2. "Cautious" Bayes; 7:16; Setting up a Bayesian classifier. Changing the laws of distribution of feature values. Verification of keyboard handwriting images of 32 subjects based on the sequential application of the modified Bayes hypothesis formula. Estimation of the probabilities of errors of the 1st and 2nd types. Plotting error graphs (ROC curves). The Bayesian classification algorithm used in this example differs from the “naive” one and was first described in [Epifantsev B.N., Lozhnikov P.S., Sulavko A.E. An algorithm for identifying hypotheses in the space of low-informative features based on the sequential application of Bayes' formula // Interindustry information service / FSUE "VIMI" - Moscow: 2013, No. 2. P. 57-62]: http://elibrary.ru/item.asp? id=19040432 https://www.youtube.com/watch?v=MdvAGp02FsY; 1.3. Checking the law of distribution of a characteristic; 4:52; Testing the hypothesis about the law of distribution of attribute values on small samples using the Pearson chi-square method with the Yates correction. For large samples (more than 200 values), the Yates correction may not be used. The example demonstrates how to find the closest distribution law presented in the program https://youtu.be/GYK7fuThoUo; 1.4. Feature extraction from speech signals (based on traditional analysis methods); 15:42; Work in the module for analyzing “raw” data. Analysis of time series using traditional methods using speech signals as an example. Loading marked speech images. Extraction of features from speech images (key phrases and passwords spoken by speakers): rough estimation of the frequency of transitions through “zero”, calculation of the autocorrelation function of the speech signal, removal of uninformative sections of the signal, construction and normalization by duration of mel-cepstrograms (extraction of mel-cepstral coefficients) . Saving image descriptions as feature vectors in the form of an xml file https://youtu.be/6wJWMVlbW-s; 1.5. Assessing the informativeness and correlation of features; 5:04; Assessing the information content of features. Construction of a correlation matrix of features (assessment of the level of cross-correlation of features). Using the example of a speech features of speakers [Deep and Wide Neural Networks] https://www.youtube.com/watch?v=zybJmTLLH-E&t=2s; 2.1.Neural network constructor: Classification of Images of Numbers (MNIST Database); 8:17; Construction of a multilayer neural network from convolutional and fully connected layers for image identification (one-to-many comparison). Training a neural network and assessing the accuracy of digit identification (10 classes, from 0 to 9) based on the MNIST dataset. Saving the structure of the neural network as well as the parameters of the trained neural network. https://www.youtube.com/watch?v=Q686ldpxzdM&t=1s; 2.2. Neural network constructor: analysis and classification of number sounds (Jakobovski database); 16:29; Loading and editing a multilayer neural network of fully connected and convolutional layers for time series classification. Loading a dataset of sounds. Preprocessing of time series and construction of spectrograms. Estimating error rates and accuracy in classifying digits from 0 to 9 based on the Jakobovski dataset. https://youtu.be/EI4RL9CN7vE; 2.3. Extracting features from speech signals using autoencoders; 20:59; Construction of an autoencoder in a neural network designer (a convolutional neural network for reducing the dimension of input data or feature space, consisting of two parts: an encoder and a decoder). Preprocessing of speech images: converting signals into averaged spectra*. Training an autoencoder using averaged spectra of speech signals. Extracting features from speech images using an encoder. *in the presented example, the energies of the spectra are arranged in descending order of frequency, from high to low https://youtu.be/UeifXThY1N4; 2.4 Classic neural network converters biometrics-code (classic fuzzy neuro-extractor); 10:40; Neural network biometric-to-code converters (BCC) are based on broad neural networks and are used to link cryptographic keys and passwords to the user’s biometric image. Synthesis, automatic learning (according to GOST 52633.5), and testing of NPBC are demonstrated using the example of the task of verifying handwritten signatures (signer authentication using handwritten images). In accordance with GOST 52633.5, training should be carried out on a sample of 11 (or more, recommended from 20) examples of the user’s image (genuine) and 64 (or more) examples of images that do not belong to the user (impostor). Testing and training were carried out both in normal mode (without protecting neural network containers) and in protected mode (after training, the neurons were lined up in a chain, after which the tables of connections and weights of each neuron were encrypted using the hash of the outputs of all previous neurons in the chain). In normal mode, the hacker has an implicit indicator of the proximity of codes generated from Impostors images to the user's key, since the stability of Impostors codes is related to the Hamming distance of these codes to the correct key. In protected execution mode, this problem is solved (the connection becomes insignificant) [Model ensembles]